help please?

Question

5a - 2b = 10
2a - 3b = -11


and

3x - 4y = 16
5x + 6y = 14


thank you<3

Well this is in Algebra 1
8th grade

Answer 1

These are systems of linear equations. The way to solve them is to isolate one variable in one equation, then make a substitution into the other.

5a - 2b = 10
2a - 3b = -11

The first equation can be re-arranged to get

b = ( 5a - 10 ) / 2

The second equation is

2a - 3b = -11

Substitute the above for b...

2a - 3 ( ( 5a - 10 ) / 2 ) = -11

...and simplify...

2a - ( 15 a - 30 ) / 2 = -11
4a - 15a + 30 = -22
-11a = -52
a = 52 / 11

Then use the original substitution to find b

b = ( 5a - 10 ) / 2

Substitute what we just got for a...

b = ( 5 * 52 / 11 - 10 ) / 2

... and simplify...

b = ( 260 / 11 - 10 ) / 2
b = ( 150 / 11 ) / 2
b = 150 / 22
b = 75 / 11

So the answers are a = 52 / 11 and b = 75 / 11.

Checking:

5a - 2b = 10
5 ( 52 / 11 ) - 2 ( 75 / 11 ) = 10
260 / 11 - 150 / 11 = 10
110 / 11 = 10
10 = 10

2a - 3b = -11
2 ( 52 / 11 ) - 3 ( 75 / 11 ) = -11
104 / 11 - 225 / 11 = -11
-121 / 11 = -11
-11 = -11

The second problem is solved in a similar fashion :)

Answer 2

You have to solve for each variable seperately.

Solve for A

5a-2b=10
5a-2b+2b=10+2b
5a=10+2b
Divide both sides by 5
a= 2+2/5b

Then substitute "A" into the next equation.
2(2+2/5b)-3b=-11
4+4/5b-3b=-11
4-4+(-2 1/5b)=-11-4
-2 1/5b=-15
Multiply by -1
2.2b=15
Divide both sides by 2.2
b=6.81 repeating

Now that you have a value for "B" go back and substitute the number for "B."

5a-2(6.81 repeating)=10
5a-13.63 repeating=10
5a-13.63 repeating+13.63 repeating=10+13.63 repeating
5a=23.63repeating
Divide both sides by 5
a=4.72 repeating

I don't have a calculator that does fractions SORRY! You'll have to figure out the fractions yourself. Do the same steps for the second problem. I did them on paper. I hope these are right. I followed the steps from wikipedia.

Answer 3

5a-2b=10
2a-3b=-11

(5a-2b)+(2a-3b)=10+(-11)
(5a-2b)+(2a-3b)=-1
5a+(2a-1b)=-1
5a+2a=-1+1b
5a+2a=-1+b
7a=-1+b
a=(-1+b)/7
a=-7+7b
a=6b
SO
5a-2b=5(6b)-2b=10
5(6b)-2b=10
30b-2b=10
28b=10
b=10/28
b=5/14
a=6(5/14)
you can figure it out frm there lol

3x-4y = 16
5x+6y = 14
(3x-4y)+(5x+6y)=16+14
(3x-4y)+(5x+6y)=30
3x+5x+10y=30
8x+10y=30
10y=30-8x
y=(30-8x)/10
y=3-8x/10


i donno if these r rite...wut grade r u in and wut corse is this in?

Answer 4

I DONT UNDERSTAND